[remcob]

This holds true for regular travel nearing light speed too: For an external observer the spaceship never goes faster than light, but the passengers clocks slow down and they can experience arbitrarily high faster-than-light speeds.

For some reason I never see this discussed when people talk about FTL travel, maybe I'm wrong?

[bno1]

It's because distances and time durations contract the faster you travel. The passangers don't experience faster than light speeds, just shorter distances.

This is how the twin paradox gets solved. The twin that leaves earth sees the trip as if it was shorter in both directions, so from their perspective it makes sense that they aged less than the twin that remained on earth.

Also, if you had infinite energy and you could travel at the speed of light you wouldn't feel any movement or time passing during your trip, it would feel like instantly teleporting from one place to another. Photons wouldn't feel their existence if they could. From their perspective they are produced in one place and instantly absorbed in another place.

[hiptobecubic]

I think because we use words like "faster" to mean "more stuff in less time," not just "feels like less time to you, but isn't."

[pcl]

Orson Scott Card’s sequels to Ender’s Game take this into account.